How do I stop a cat from scratching it's claws on the sofa?

I agree with LadyWolf; you must offer your cat another place in which to scratch.

Cats scratch for a couple different reasons: one is to shed the outer cuticle of the nail, one is to stretch their muscles and the other is to mark territory. That being said, it should be obvious that cats leave scent behind after scratching. They return to that spot which holds the scent to scratch more.

I do not condone any "swatting" or other physical punishment for cats. They will associate YOU with that negativity, and not neccessarily the behavior.

A squirt bottle, such as hannzach suggested could work (as long as they don't associate you with the water) but also make sure that the spot your cat has been scratching is unappealing. Putting double sided sticky tape on the spot(s) and then offering a scratching post right in front of the sofa will most often deter a cat from ripping your furniture to shreds.

A variety of places to scratch and also a variety of substrates on which to claw should do the trick. Be consistent, avoid punishment and reward your cat's good behavior with catnip on the new scratching post or rug.

You and your cat will be most pleased with the results!

The best way to stop a cat from scratching undesirable objects is to provide a new spot for them to scratch.

Carpet remnants are a good option. Placing a bit of carpet on a piece of wood or sturdy cardboard and supporting it against a wall, or placing it on a base will provide your kitty with a new place to scratch. You could also purchase a commercial cat scratching post.

Catnip on the carpet should attract the cat to begin scratching there, if not, try placing the carpet in front of the area where the cat is already scratching.

Scolding is not a bad idea either, or a swat, it has worked for all cats I have owned over many years, they are much like children, they know what they can get by with, but wood covered with carpet will sometimes work too, I think personally,they prefer the wood and the smell of it is what draws them.I had a cat once that knew she could not scratch my crochet pieces she loved to lay on so she would watch me and just press her paws into it to her hearts content but she never let the claws out.

When your cat has found a favourite scratching place, it can be hard to stop them using the same place. My cat keeps scratching the corners of the carpet, so I've found giving her a quick spray of water from a spray bottle does help. Then they start to associate the scratching with being sprayed with water, and hopefully will stop.